There are many different graphic programs that can be used - I have in the past done mine using adobe photoshop and then also using adobe elementals, earlier I used paintshop pro, - I know there are now much easier aplpications that can be used, I think many businesses used Corel Draw as that provides an excellent output for graphic printers , although that may show my age a bit

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Basically any graphic program should be able to get you started, but I think you should just draw your basic logo initially , and than take a picture of it and bring that into a graphic program - makes it easier , unless you are real handy with graphic apps, and have a sketching tablet (those are cool )